1. Field of the Invention
The present invention relates to an optical modulator which is made of substances having electro-optic effects and comprises a guide structure having an optical waveguide between two opposite traveling-wave type electrodes, and particularly to a wide-band optical modulator which exhibits a wide band, a small driving voltage, and high modulation efficiency and which is capable of obtaining complete matching of the phase velocity of an optical wave with that of a modulating wave.
2. Description of the Related Art
An optical modulator is an element used for causing the strength and the phase of an optical wave to be changed in accordance with signals and is one of the most fundamental active devices in optical communication and optical information processing.
Since an optical modulator and an optical switch are required to function in a wide band, at a super-high speed, and with a lower driving power, a wave guide-type element has been developed which employs electro-optic effects fundamentally showing a high operating speed and which can obtain a characteristic of high efficiency.
In addition, it has been thought that a configuration employing traveling-wave type electrodes is excellent for making a wide band optical modulator or optical switch or for achieving very high speed, and various kinds of such configuration have been proposed, as described below.
In general, with respect to an optical modulator having traveling-wave type electrodes in which an optical waveguide is made of a substance having electro-optic effects, the following equations apply.
If the refractive index of the wave guide for an optical wave is n.sub.o and the equivalent refractive index of the substance having electro-optic effects for a modulated wave is n.sub.m, the phase velocities V.sub.o, V.sub.m of the optical wave and the modulating wave are expressed by the following equation (1): EQU V.sub.o =C.sub.o /n.sub.o, V.sub.m =C.sub.o /n.sub.m ( 1)
wherein C.sub.o is the velocity of light in vacuum.
If the bandwidth of "3dB down" modulation by means of the traveling-wave operation is fm and the length of the electrodes is, the equation (2) is established. ##EQU1##
Namely, it can be seen that the upper bound of the modulation bandwidth or the high-speed modulation frequency is limited by the difference between n.sub.m and n.sub.o.
The n.sub.o value is the value of refractive index of the optical waveguide, while if the capacitance per unit length of the electrodes is C, the equivalent refractive index n.sub.m for the modulating wave is expressed by the following equation (3): EQU n.sub.m =(C/C.sub.o).sup.1/2 ( 3)
wherein C.sub.o is the capacitance per unit length when the substance having electro-optic effects is replaced in vacuum.
In addition, the driving power P necessary for 100% modulation is expressed by the following equation (4): EQU P=V.sub..pi..sup.2 /Z.sub.o ( 4)
wherein V.sub..pi., Z.sub.o are the half-wave voltage and the characteristic impedance of the electrodes and are expressed by the equations (5) and (6), respectively: EQU V.sub..pi. =.lambda..sub.o.g/n.sub.o.sup.3.r.GAMMA...beta. (5) EQU Z.sub.o =1/C.sub.o.n.sub.m.C.sub.o ( 6)
wherein .lambda..sub.o is a free space optical wavelength; g, the distance between electrodes; r, an electro-optic constant; and .GAMMA., a superimposed integral coefficient of the modulation electric field and the strength of the guided optical wave which depends upon the shapes of electrodes and thus is called a field correction factor within the range of 0&lt;.GAMMA..ltoreq.1.
The characteristics of conventional optical modulators are described in detail below on the basis of the above-described equations (1) to (6).
An optical modulator shown in FIG. 11 is one which is conventionally most widely used and which comprises an optical waveguide (11) provided in the vicinity of the surface of a LiNbO.sub.3 crystal substrate (10) in a given direction, planar type traveling-wave electrodes (12) having asymmetrical forms and adhered to the surface of the substrate (10) so as to hold the optical waveguide (11) therebetween, a power source for modulation (13) connected to one end of each traveling-wave electrode (12), and a resistance (14) provided at the terminal of each traveling-wave electrode (12).
The modulating wave supplied from the modulation power source (13) progresses on the traveling-wave electrodes (12) at a phase velocity V.sub.m and is consumed as heat by the resistance (14) so that it is not returned to the power source side (3).
A ray of incident light (15) progresses in the optical waveguide (11) at a phase velocity V.sub.o and is subjected to modulation by the traveling-wave modulation field.
In order to obtain high efficiency, the refractive index for extraordinary rays is often used in the optical waveguide comprising the LiNbO.sub.3 crystal substrate, and thus n.sub.o =2.20.
If the dielectric constants of LiNbO.sub.3 .epsilon..sub.1 =43, .epsilon..sub.3 =28 are used, the following equation is obtained from the equation (3) ##EQU2## wherein .epsilon..sub.E is called an effective dielectric constant. From the calculations made by an exact successive over-relaxation method, EQU n.sub.m .perspectiveto.4.28
Therefore, when n.sub.o =2.20 and n.sub.m =4.20 are substituted into the equations (1) and (2), EQU V.sub.o /V.sub.m =1.95 EQU fm.multidot.l.perspectiveto.9.2 GHz.multidot.cm
are obtained.
In other words, it is found that the optical modulator shown in FIG. 11 shows a disadvantage in that, when the length of each electrode l=1 cm, bandwidths above 9.2 GHz or high speed modulation at above 9.2 GHz cannot be obtained because the velocity of the optical wave is 1.95 times that of the modulating wave.
In addition, if the width of the widest electrode of the traveling-wave electrodes (12) is semi-infinite, the width of the narrow electrode is W, and the distance between the electrodes is g, when W/g.perspectiveto.1.5, Z.sub.o =50.OMEGA. and matching of the feeding system is thus obtained.
However, if the W/g value is changed, the fm value is not changed because of the constant value of n.sub.m .perspectiveto.4.2.
In addition, planar type traveling-wave electrodes generally show disadvantages with respect to having a small value of .GAMMA., which may be as small as &lt;0.4, a large value of V.sub..pi., and low modulation efficiency.
Furthermore, there is an important problem in creating a band limit with respect to an absorption loss of the modulating wave by the electrode resistance. Thus, the thickness of the electrodes is required to be a skin depth (about 3 .mu.m in Al or Au electrodes) or more.
It is found from the equation (5) that g is required to be reduced in order to reduce V.sub..pi., but, since Z.sub.o =50.OMEGA., there is a limit of W/g=1.5 and the width of the electrode is thus extremely small, leading to an increase in resistance.
Since .GAMMA. is reduced as g is reduced and, owing to manufacturing limits, the thickness of the electrode is required to be reduced as g is reduced, the above-described planar-type electrodes show disadvantages in that the modulation bandwidth is reduced as efficiency is improved.
The optical modulator shown in FIG. 12 has a similar configuration to that of the optical modulator shown in FIG. 11, in which, since the phases of traveling-wave electrodes (16) are periodically reversed, an optical waveguide (11) lies in a periodical zig-zag and the sign of an electrical field applied to the optical waveguide (11) is reversed.
In this optical modulator, when the modulation frequency is sufficiently low, the sign of the phase to be modulated is changed in each period and light is slightly modulated.
On the other hand, when the frequency is increased and a wavelength becomes the period of the electrodes, the periodic portion of the negative (or positive) electrical field is reversed by the turn of the electrodes and thus only a positive (or negative) electrical field is constantly applied to light, without any deterioration of the modulation efficiency.
In addition, when a frequency is further increased, the wavelength in the modulation field is decreased and deviates from the turning period of the electrodes, again leading to deterioration of the modulation efficiency.
Therefore, it is fundamentally difficult to obtain a wide band characteristic in the configuration shown in FIG. 12. The shape of the electrodes reduces the width of the effective modulation region and increases the resistance of the electrodes, and the planar shape reduces the .GAMMA. value and thus decreases efficiency. There are certain problems in that the characteristic impedance Z.sub.o shows a change and in that the forming of the electrodes requires many process steps and is difficult to perform.
The optical modulator shown in FIG. 13 has a branched interference-type configuration in which a groove portion (18) is provided between the branched portions of an optical guide (17) which branches into two guides in the middle of the guide on a substrate (10), and in which a light output is subjected to strength modulation. Traveling-wave electrodes (12) have asymmetrical shapes and the modulation characteristic is determined by the phase modulation characteristic.
In such a configuration, the groove portion (18) provided therein causes components in an electrical field to leak into the air and reduces the equivalent refractive index n.sub.m of a modulating wave.
Even if the shape of the groove portion (18) is changed into various forms, there is a limit on n.sub.m. For example, when a groove having a width of 6 .mu.m and a depth of 6 .mu.m is provided on a LiNbO.sub.3 substrate, n.sub.m is reduced to about 3.8 and by the equation (2), EQU f.sub.m l.perspectiveto.12 GHz.multidot.cm,
with the bandwidth being increased by about 30% as compared with a case in which no groove is provided.
However, as described above, since the field components leak to the groove portion, the .GAMMA. value is reduced further, decreases even more as the band is made wider, and becomes as small as &lt;0.35, as compared with the case of a planar-type electrode without any groove.
The optical modulator shown in FIG. 14 is provided with a LiTaO.sub.3 crystal C-plate substrate and traveling-wave electrodes (22) having reverse L-shaped sections, in which two SiO.sub.2 plates (21) are disposed on the substrate (20) so as to hold an optical guide (11) therebetween, the traveling-wave electrodes (22) having reverse L-shaped sections being provided on the upper surfaces and the opposite surfaces thereof. The characteristic impedance Z.sub.o and the equivalent refractive index n.sub.m can be changed by changing the width L and the height H of each electrode to various values.
If the width of the electrodes is increased, n.sub.m becomes maximum and is then gradually decreased.
On the other hand, since Z.sub.o is slowly reduced, matching is obtained at Z.sub.o =50.OMEGA. at a suitable value of L. At this time, the greater the H value becomes, the greater is the L value.
In addition, if L is reduced, n.sub.m is reduced as H increases, but conversely, Z.sub.o is rapidly increased, and no matching is thus obtained in a 50.OMEGA. system. It is seen from this that there is a lower limit on n.sub.m.
Therefore, as an appropriate example of design, when H=5 .mu.m, L=200 .mu.m, g=50 .mu.m, Z.sub.o =50.OMEGA., n.sub.m =3.5 and from the equation (2), EQU f.sub.m .multidot.l=14.7 GHz.multidot.cm.
The bandwidth of the optical modulator shown in FIG. 14 is thus about 1.6 times that of the optical modulator shown in FIG. 11.
In such a configuration, however, it is difficult to cause the velocity of the optical wave to be matched with that of the modulated wave and simultaneous matching of the characteristic impedance is very difficult.
In addition, since the components of the modulation field leak into the SiO.sub.2 plates (21) and the air layer which are close to the electrodes (22), n.sub.m is reduced, but there is a weak relation to the optical waveguide (11) and the .GAMMA. value is thus substantially the same as that of the above-described planar-type electrodes.
There is also a disadvantage in that the distance between the electrodes is limited by the matching of impedance and it is thus difficult to reduce the distance, resulting in an increased V.sub..pi. value.
The optical modulator shown in FIG. 15 comprising a so-called ridge-type optical waveguide is characterized in that an optical guide (23) of a convex strip shape is provided on a substrate (10), and an optical waveguide (23) having a rectangular section makes the ratio of confinement of light energy good, enables its size to be made small without any limit on diffraction, and facilitates the formation of an optical waveguide of any pattern such as a bend.
In particular, when the material of the substrate is LiNbO.sub.3, the electrode configuration comprising lumped-parameter type electrodes (12a) having L-shaped sections makes it possible for the .GAMMA. value to be made sufficiently large, whereby it is possible to make the efficiency high and make the driving voltage low.
Since the ridge-form optical modulator shown in FIG. 15 has the optical waveguide (23) having a rectangular section, it can solve the various problems experienced with the above-described optical modulators shown in FIGS. 11 to 14. However, since n.sub.m is as large as &gt;4.2 and Z.sub.o &gt;50.OMEGA., there are disadvantages in that it is impossible to completely match the phase velocity of the optical wave with that of the modulating wave and the matching of impedance is difficult.